The U.S. share of world stock market valuation has slipped. Meanwhile, emerging markets have gained, with Asian bourses the biggest winners.

Like urbanites' perennial search for the next up-and-coming neighborhood, investors are looking—and moving—beyond the U.S. for better deals. The U.S. share of the world stock market valuation has dropped by a substantial 1.3 percentage points since hitting a post-recession high of nearly 37% in mid-March. That's an unusually large drop in such a short period of time, according to Bespoke...